349 lines
12 KiB
Python
349 lines
12 KiB
Python
"""
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Task 3 - Step 6: 效果评估
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=========================
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输入:
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- 04_reschedule.xlsx (访问次数)
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- 03_allocation.xlsx (配对分配方案)
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- ../task1/03_allocate.xlsx (Task 1结果，用于对比)
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- ../task1/04_metrics.xlsx (Task 1指标，用于对比)
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输出: 06_evaluate.xlsx (评估指标对比)
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评估指标:
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- E1': 期望总服务量
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- E2': 质量加权服务量（总量计算衰减）
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- F1': 满足率Gini系数
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- F2': 最低满足率
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- R1: 服务缺口风险
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- RS: 资源节省率
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有效性衰减公式（总量计算）:
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q(μ_i + μ_j) = min(1, 250 / (μ_i + μ_j))
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"""
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import pandas as pd
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import numpy as np
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from scipy import stats
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# ============================================
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# 参数设置
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# ============================================
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RESCHEDULE_FILE = '04_reschedule.xlsx'
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ALLOCATION_FILE = '03_allocation.xlsx'
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TASK1_ALLOC_FILE = '../task1/03_allocate.xlsx'
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TASK1_METRIC_FILE = '../task1/04_metrics.xlsx'
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OUTPUT_FILE = '06_evaluate.xlsx'
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Q = 400 # 卡车容量
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QUALITY_THRESHOLD = 250 # 质量衰减阈值
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SHORTFALL_THRESHOLD = 0.8 # 服务缺口阈值
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# ============================================
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# 辅助函数
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# ============================================
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def quality_factor(mu_total):
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"""质量折扣因子（总量计算）"""
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return min(1.0, QUALITY_THRESHOLD / mu_total) if mu_total > 0 else 1.0
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def expected_service(q, mu, sigma):
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"""E[min(D, q)]"""
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if sigma == 0:
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return min(mu, q)
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z = (q - mu) / sigma
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return mu * stats.norm.cdf(z) - sigma * stats.norm.pdf(z) + q * (1 - stats.norm.cdf(z))
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def gini_coefficient(values):
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"""计算Gini系数"""
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values = np.array(values)
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values = values[~np.isnan(values)]
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if len(values) == 0:
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return 0
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values = np.sort(values)
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n = len(values)
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cumsum = np.cumsum(values)
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return (2 * np.sum((np.arange(1, n + 1) * values)) - (n + 1) * cumsum[-1]) / (n * cumsum[-1]) if cumsum[-1] > 0 else 0
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def shortfall_probability(q, mu, sigma, threshold=0.8):
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"""P(S/D < threshold)，即服务不足的概率"""
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# 简化计算：P(min(D,q) / D < 0.8) ≈ P(D > q/0.8)
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if sigma == 0:
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return 0 if q >= mu * threshold else 1
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critical_demand = q / threshold
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return 1 - stats.norm.cdf((critical_demand - mu) / sigma)
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# ============================================
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# 读取数据
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# ============================================
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print("=" * 60)
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print("Task 3 - Step 6: 效果评估")
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print("=" * 60)
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# Task 3 数据
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df_sites = pd.read_excel(RESCHEDULE_FILE, sheet_name='sites_schedule')
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df_pairs = pd.read_excel(ALLOCATION_FILE, sheet_name='allocation')
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df_pair_visits = pd.read_excel(RESCHEDULE_FILE, sheet_name='pair_visits')
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print(f"\n读取Task 3数据:")
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print(f" - 站点数: {len(df_sites)}")
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print(f" - 配对数: {len(df_pairs)}")
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# Task 1 数据（用于对比）
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df_task1 = pd.read_excel(TASK1_ALLOC_FILE)
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try:
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df_task1_metrics = pd.read_excel(TASK1_METRIC_FILE)
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has_task1_metrics = True
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except:
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has_task1_metrics = False
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print(" - 未找到Task 1指标文件，将重新计算")
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# ============================================
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# 计算 Task 3 指标
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# ============================================
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print(f"\n" + "-" * 40)
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print("计算 Task 3 指标")
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print("-" * 40)
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# 合并配对访问信息
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pair_k = {(row['site_i_id'], row['site_j_id']): row['k_dual']
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for _, row in df_pair_visits.iterrows()}
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# === E1': 期望总服务量 ===
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E1_prime = 0
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# 单站点贡献
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for _, row in df_sites.iterrows():
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k_single = row['k_single_final']
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mu = row['mu']
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E1_prime += k_single * mu
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# 双站点贡献
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for _, row in df_pairs.iterrows():
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pair_key = (row['site_i_id'], row['site_j_id'])
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k_dual = pair_k.get(pair_key, 0)
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E_total = row['E_total']
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E1_prime += k_dual * E_total
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print(f"E1' (期望总服务量): {E1_prime:.0f}")
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# === E2': 质量加权服务量 ===
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E2_prime = 0
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# 单站点贡献
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for _, row in df_sites.iterrows():
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k_single = row['k_single_final']
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mu = row['mu']
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q_factor = quality_factor(mu)
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E2_prime += k_single * q_factor * mu
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# 双站点贡献（总量计算衰减）
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for _, row in df_pairs.iterrows():
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pair_key = (row['site_i_id'], row['site_j_id'])
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k_dual = pair_k.get(pair_key, 0)
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mu_sum = row['mu_i'] + row['mu_j']
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E_total = row['E_total']
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q_factor = quality_factor(mu_sum) # 总量计算
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E2_prime += k_dual * q_factor * E_total
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print(f"E2' (质量加权服务量): {E2_prime:.0f}")
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# === 满足率计算 ===
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# Task 1定义: r_i = k_i * μ_i / μ̃_i (等效服务次数)
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# Task 3: 需要分别计算单站点和双站点的贡献
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site_satisfaction = {}
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for _, row in df_sites.iterrows():
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site_id = row['site_id']
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mu = row['mu']
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mu_tilde = row['mu_tilde']
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k_single = row['k_single_final']
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# 单站点贡献: k_single * μ / μ̃
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r_single = k_single * mu / mu_tilde if mu_tilde > 0 else 0
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site_satisfaction[site_id] = r_single
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# 加上双站点贡献
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for _, row in df_pairs.iterrows():
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pair_key = (row['site_i_id'], row['site_j_id'])
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k_dual = pair_k.get(pair_key, 0)
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# 双站点贡献: k_dual * E[S_i] / μ̃_i
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mu_tilde_i = df_sites[df_sites['site_id'] == row['site_i_id']]['mu_tilde'].values[0]
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mu_tilde_j = df_sites[df_sites['site_id'] == row['site_j_id']]['mu_tilde'].values[0]
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r_dual_i = k_dual * row['E_Si'] / mu_tilde_i if mu_tilde_i > 0 else 0
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r_dual_j = k_dual * row['E_Sj'] / mu_tilde_j if mu_tilde_j > 0 else 0
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site_satisfaction[row['site_i_id']] += r_dual_i
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site_satisfaction[row['site_j_id']] += r_dual_j
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# 计算满足率列表
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satisfaction_rates = list(site_satisfaction.values())
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# === F1': Gini系数 ===
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F1_prime = gini_coefficient(satisfaction_rates)
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print(f"F1' (满足率Gini): {F1_prime:.4f}")
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# === F2': 最低满足率 ===
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F2_prime = min(satisfaction_rates) if satisfaction_rates else 0
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print(f"F2' (最低满足率): {F2_prime:.4f}")
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# === R1: 服务缺口风险 ===
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# 双站点访问时，任一站点服务不足的概率
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shortfall_probs = []
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for _, row in df_pairs.iterrows():
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q_final = row['q_final']
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mu_i, sigma_i = row['mu_i'], row['sigma_i']
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mu_j, sigma_j = row['mu_j'], row['sigma_j']
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# 站点i的缺口概率
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p_i = shortfall_probability(q_final, mu_i, sigma_i, SHORTFALL_THRESHOLD)
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# 站点j的缺口概率
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p_j = shortfall_probability(Q - q_final, mu_j, sigma_j, SHORTFALL_THRESHOLD)
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# 至少一个站点缺口的概率
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p_either = 1 - (1 - p_i) * (1 - p_j)
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shortfall_probs.append(p_either)
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R1 = np.mean(shortfall_probs) if shortfall_probs else 0
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print(f"R1 (平均缺口风险): {R1:.4f}")
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# === RS: 资源节省率 ===
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total_dual = df_pair_visits['k_dual'].sum()
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RS = total_dual / 730 * 100
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print(f"RS (资源节省率): {RS:.2f}%")
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# ============================================
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# 计算 Task 1 指标（用于对比）
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# ============================================
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print(f"\n" + "-" * 40)
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print("计算 Task 1 指标（对比基准）")
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print("-" * 40)
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# E1: 总服务量
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E1_task1 = (df_task1['k'] * df_task1['mu']).sum()
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print(f"E1 (Task 1 总服务量): {E1_task1:.0f}")
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# E2: 质量加权
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E2_task1 = 0
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for _, row in df_task1.iterrows():
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q_factor = quality_factor(row['mu'])
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E2_task1 += row['k'] * q_factor * row['mu']
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print(f"E2 (Task 1 质量加权): {E2_task1:.0f}")
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# F1: Gini系数 - 使用与Task 3相同的r定义
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# r_i = k_i * μ_i / μ̃_i
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task1_rates = []
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for _, row in df_task1.iterrows():
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r = row['k'] * row['mu'] / row['mu_tilde'] if row['mu_tilde'] > 0 else 0
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task1_rates.append(r)
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F1_task1 = gini_coefficient(task1_rates)
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print(f"F1 (Task 1 Gini): {F1_task1:.4f}")
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# F2: 最低满足率
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F2_task1 = min(task1_rates) if task1_rates else 0
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print(f"F2 (Task 1 最低满足率): {F2_task1:.4f}")
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# ============================================
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# 对比分析
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# ============================================
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print(f"\n" + "-" * 40)
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print("Task 3 vs Task 1 对比")
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print("-" * 40)
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comparison = pd.DataFrame({
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'Metric': ['E1 (总服务量)', 'E2 (质量加权)', 'F1 (Gini系数)', 'F2 (最低满足率)'],
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'Task 1': [E1_task1, E2_task1, F1_task1, F2_task1],
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'Task 3': [E1_prime, E2_prime, F1_prime, F2_prime],
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'Change': [E1_prime - E1_task1, E2_prime - E2_task1,
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F1_prime - F1_task1, F2_prime - F2_task1],
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'Change %': [(E1_prime - E1_task1) / E1_task1 * 100,
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(E2_prime - E2_task1) / E2_task1 * 100,
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(F1_prime - F1_task1) / F1_task1 * 100 if F1_task1 != 0 else 0,
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(F2_prime - F2_task1) / F2_task1 * 100 if F2_task1 != 0 else 0]
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})
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print(comparison.to_string(index=False))
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# ============================================
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# 保存结果
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# ============================================
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with pd.ExcelWriter(OUTPUT_FILE, engine='openpyxl') as writer:
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# Sheet 1: 指标对比
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comparison.to_excel(writer, sheet_name='comparison', index=False)
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# Sheet 2: Task 3 详细指标
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task3_metrics = pd.DataFrame({
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'metric': ['E1_prime', 'E2_prime', 'F1_prime', 'F2_prime',
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'R1', 'RS', 'total_pairs', 'total_dual_visits'],
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'value': [E1_prime, E2_prime, F1_prime, F2_prime,
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R1, RS/100, len(df_pairs), total_dual],
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'description': ['期望总服务量', '质量加权服务量', '满足率Gini系数', '最低满足率',
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'平均缺口风险', '资源节省率', '配对数', '双站点访问次数']
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})
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task3_metrics.to_excel(writer, sheet_name='task3_metrics', index=False)
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# Sheet 3: 站点级别满足率
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site_rates = []
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for site_id, r in site_satisfaction.items():
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site_row = df_sites[df_sites['site_id'] == site_id]
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if len(site_row) > 0:
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site_name = site_row['site_name'].values[0]
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mu = site_row['mu'].values[0]
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mu_tilde = site_row['mu_tilde'].values[0]
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k_single = site_row['k_single_final'].values[0]
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k_dual = site_row['k_dual'].values[0]
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else:
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site_name = f"Site_{site_id}"
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mu, mu_tilde, k_single, k_dual = 0, 0, 0, 0
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site_rates.append({
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'site_id': site_id,
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'site_name': site_name,
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'mu': mu,
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'mu_tilde': mu_tilde,
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'k_single': k_single,
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'k_dual': k_dual,
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'satisfaction_rate_r': r
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})
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df_site_rates = pd.DataFrame(site_rates)
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df_site_rates = df_site_rates.sort_values('satisfaction_rate_r')
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df_site_rates.to_excel(writer, sheet_name='site_satisfaction', index=False)
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# Sheet 4: 配对风险分析
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pair_risk = []
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for idx, row in df_pairs.iterrows():
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pair_key = (row['site_i_id'], row['site_j_id'])
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k_dual = pair_k.get(pair_key, 0)
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q_final = row['q_final']
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mu_i, sigma_i = row['mu_i'], row['sigma_i']
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mu_j, sigma_j = row['mu_j'], row['sigma_j']
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p_i = shortfall_probability(q_final, mu_i, sigma_i, SHORTFALL_THRESHOLD)
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p_j = shortfall_probability(Q - q_final, mu_j, sigma_j, SHORTFALL_THRESHOLD)
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pair_risk.append({
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'site_i_name': row['site_i_name'],
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'site_j_name': row['site_j_name'],
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'k_dual': k_dual,
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'q_final': q_final,
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'shortfall_prob_i': p_i,
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'shortfall_prob_j': p_j,
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'shortfall_prob_either': 1 - (1 - p_i) * (1 - p_j)
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})
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df_pair_risk = pd.DataFrame(pair_risk)
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df_pair_risk = df_pair_risk.sort_values('shortfall_prob_either', ascending=False)
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df_pair_risk.to_excel(writer, sheet_name='pair_risk', index=False)
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print(f"\n结果已保存至: {OUTPUT_FILE}")
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print(" - Sheet 'comparison': Task 1 vs Task 3 对比")
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print(" - Sheet 'task3_metrics': Task 3 详细指标")
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print(" - Sheet 'site_satisfaction': 站点满足率")
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print(" - Sheet 'pair_risk': 配对风险分析")
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print("\n" + "=" * 60)
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